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A325211
a(1) = 1; a(n) = Sum_{d|n, d<n} tau(n/d) * a(d), where tau = A000005.
1
1, 2, 2, 7, 2, 12, 2, 24, 7, 12, 2, 58, 2, 12, 12, 82, 2, 58, 2, 58, 12, 12, 2, 256, 7, 12, 24, 58, 2, 104, 2, 280, 12, 12, 12, 355, 2, 12, 12, 256, 2, 104, 2, 58, 58, 12, 2, 1072, 7, 58, 12, 58, 2, 256, 12, 256, 12, 12, 2, 652, 2, 12, 58, 956, 12, 104, 2, 58, 12, 104
OFFSET
1,2
FORMULA
G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} tau(k) * A(x^k).
a(p) = 2, where p is prime.
MATHEMATICA
a[n_] := If[n == 1, n, Sum[If[d < n, DivisorSigma[0, n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 70}]
nmax = 70; A[_] = 0; Do[A[x_] = x + Sum[DivisorSigma[0, k] A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
PROG
(PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n] = sumdiv(n, d, v[d]*numdiv(n/d))); v} \\ Andrew Howroyd, Sep 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 05 2019
STATUS
approved